Yes.
And I cite as my evidence: the real world.
Population growth by birth rate is negative in high-amenity Europe.
Population growth by birth rate in Africa, where the only resources they have is space and nature: explosive.
Quod erat demonstradum.
I think you have no clue as to WHY these disparities exist and I can tell you one thing and it has NOTHING to do with space. My country have ALLOT of space per inhabitants and still have one of the lowest population growth there is, while countries such as the US still have a relatively high population growth among other things breaking the mould of most western countries.
Population growth is more of a social thing rather than economic or space driven... please read up on the subject before you actually try to get a point across.
Realistically most growth for colonies would come from migration for a very long time where people would migrate to a more favourable economically lucrative society. This is something we have witnesses in the past. If there are no economical or cultural reason to migrate people probably would not o so either.
Actual population growth should stem more from social factors and less from actual living space. There are no evidence that tells us people would create bigger families unless there were some incentives to do so... the huge boost in population from early 1900 until today is entirely driven by technology and progress in medicine making children survive and that created huge families... as generations grow up in a world where children survived longer people just tended to have less children as a response and that is what we have seen world wide despite economy, culture, economy and religion... unless child birth have been artificially compromised as in prohibiting birth control or as in China restricting the number of children to less than two there seem to be a pretty stable overall rate of birth and death in human population if left alone.
I suppose that you don't know that the amount of humans that live today is more than have lived through the entire history of the human species if you count from the start of the 1900.
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